The Null and Alternative Hypothesis

      The Null and Alternative Hypothesis

Written by Donald Ary et al in Introduction to Research in Education. Belmount: Wadsworth.2010. pp.91-92

I. The Null Hypothesis
It is impossible to test research hypotheses directly. You must fi rst state a null hypothesis (symbolized H0) and assess the probability that this null hypothesis is true. The null hypothesis is a statistical hypothesis. It is called the null ypothesis because it states that there is no relationship between the variables in the population.

A null hypothesis states a negation (not the reverse) of what the experimenter expects or predicts. A researcher may hope to show that after an experimental treatment, two populations will have different means, but the null hypothesis would state that after the treatment the populations’ means will not be different.

What is the point of the null hypothesis? A null hypothesis lets researchers assess whether apparent relationships are genuine or are likely  to be a function of chance alone. It states, “The results of this study could easily have happened by chance.”

Statistical tests are used to determine the probability that the null hypothesis is true. If the tests indicate that observed relationships had only a slight probability of occurring by chance, the null hypothesis becomes an unlikely explanation and the researcher rejects it. Researchers aim to reject the null hypothesis as they try to show there is a relationship between the variables of the study.

Testing a null hypothesis is analogous to the prosecutor’s work in a criminal trial. To establish guilt, the prosecutor (in the U.S. legal system) must provide sufficient evidence to enable a jury to reject the presumption of innocence beyond reasonable doubt. It is not possible for a prosecutor to prove guilt conclusively, nor can a researcher obtain unequivocal support for a research hypothesis.
The defendant is presumed innocent until sufficient evidence indicates that he or she is not, and the null hypothesis is presumed true until sufficient evidence indicates otherwise.

For example, you might start with the expectation that children will exhibit greater mastery of mathematical concepts through individual instruction than through group instruction. In other words, you are positing a relationship between the independent variable (method of instruction) and the dependent variable (mastery of mathematical concepts).

The research hypothesis is “Students taught  through individual instruction will exhibit greater mastery of mathematical concepts than students taught through group instruction.” The null hypothesis, the statement of no relationship between variables, will read “The mean mastery scores (population mean μi) of all students taught by individual instruction will equal the mean mastery scores (population mean μg) of all those taught by group instruction.” H0: μi = μg.

II. The Alternative Hypothesis
Note that the hypothesis “Children taught by individual instruction will exhibit less mastery of mathematical concepts than those taught by group instruction” posits a relationship between variables and therefore is not a null hypothesis. It is an example of an alternative hypothesis.

In the example, if the sample mean of the measure of mastery of mathematical concepts is higher for the individual instruction students than for the group instruction students, and inferential statistics indicate that the null hypothesis is unlikely to be true, you reject the null hypothesis and tentatively conclude that individual instruction results in greater mastery of mathematical concepts than does group instruction.

If, in contrast, the mean for the group instruction students is higher than the mean for the individual instruction students, and inferential statistics indicate that this difference is not likely to be a function of chance, then you tentatively conclude that group instruction is superior.

If inferential statistics indicate that observed differences between the means of the two instructional groups could easily be a function of chance, the null hypothesis is retained, and you decide that insufficient evidence exists for concluding there is a relationship between the dependent and independent variables.

The retention of a null hypothesis is not positive evidence that the null hypothesis is true. It indicates that the evidence is insufficient and that the null hypothesis,the research hypothesis, and the alternative hypothesis are all possible.